Cremona's table of elliptic curves

6720 = 2⁶ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	6720ba	Isogeny class
Conductor	6720	Conductor
∏ cp	60	Product of Tamagawa factors cp
Δ	2389782528000 = 215 · 35 · 53 · 74	Discriminant
Eigenvalues	2+ 3- 5- 7+ -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1296065,567489663]	[a1,a2,a3,a4,a6]
Generators	[661:180:1]	Generators of the group modulo torsion
j	7347751505995469192/72930375	j-invariant
L	4.9572079699012	L(r)(E,1)/r!
Ω	0.57055757374768	Real period
R	0.57922380936248	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6720m3 3360b3 20160bc3 33600bb4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720ba4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	-	+	-4	2	-2	4	0	-10	0	-6	-10	8	-4	-6	0	-10	8	-8	-2	4	12	6	6

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Quadratic twists for elliptic curve 6720ba4

-4	8	-3	5	-7
6720m3	3360b3	20160bc3	33600bb4	47040p4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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